Welcome to the first issue of the seventh volume of The Journal of Investment Strategies, in which we present four papers that I believe will be of special interest to active investors and portfolio managers while also hopefully being of interest to academic and industry researchers.
In the issue’s first paper, “Efficient trading in taxable portfolios”, Sanjiv R. Das, Dennis Yi Ding, Vincent Newell and Daniel N. Ostrov tackle the very important but relatively underexplored topic of tax-efficient portfolio management. The vast majority of standard portfolio models ignore this effect, and they are strictly speaking only applicable to nontaxable or tax-deferred investments such as those from tax-exempt institutions or from individual retirement accounts. As soon as one is dealing with taxable portfolios, the nonlinear and path-dependent nature of taxes makes this problem very nontrivial. Its impact, though, is difficult to overestimate as taxes may account for a very sizeable portion of returns – especially in the case of active management, which can generate short-term capital gains – and the difference between the pre- and after-tax returns could be extremely important.
The authors focus on a specific problem setting related to life-cycle investment management, ie, the investment strategy that changes the allocation between risky and low-/no-risk assets as the investor ages and transitions from the accumulation phase to the decumulation phase of life after retirement. To make the problem tractable, they assume that the risky asset is a non-dividend-yielding stock index and that the low-risk asset is cash. Solving the problem via a Monte Carlo simulation and optimization approach, they are able to retain the full complexity of the US tax code, including limited capital gains loss deductions, differences between short-term and long-term capital gains taxes, and the treatment of taxes upon the death of a taxpayer. They are able to demonstrate the sensitivity of the solutions to various important input parameters, including capital gains tax rates, the current cost basis, the expected rates of stock return and interest rates, the volatility of the stock, the level of transaction costs, and the (very long) time horizon of the strategy. They uncover many interesting and novel results, including a relatively counterintuitive finding that rising tax rates make the larger stock allocation more preferred rather than less so.
I believe this paper will find interested readers among the many industry practitioners working in the wealth and retirement management areas. The paper’s findings may have a significant impact on how they approach the practical management of their portfolios.
Our second paper, “Portfolio concentration and equity market contagion: evidence on the ‘flight to familiarity’ across indexing methods” by Lars Kaiser, explores the intriguing concept of “flight to familiarity” as an explanation for contagion effects in equity portfolios. The concept helps explain both similarities and differences between the large number of alternative index weighting schemes that have been discussed in the literature, and used by practitioners, over the past two decades. Some of the most prominent alternative schemes, deviating from the market capitalization weights, are the 1=N equal weight approach, the diversity weighted model, the inverse beta model, the minimum-variance model, the equal risk contribution model and the maximum-diversification model, to name but a few. The authors explore metrics including absolute and relative holdings overlap, Euclidean distance and the Bray–Curtis dissimilarity measure, and they demonstrate that the holding overlap is not sufficient to explain the correlations between the portfolios based on different weighting schemes.
Instead, a different regime-dependent pattern emerges, where one can see that in high-volatility, low-correlation states of the market, portfolios tend to become more concentrated and more similar, while in low-volatility, high-correlation states they become less similar (hence, the term “flight to familiarity”). This seems natural and intuitive and is explained by the fact that in low-risk states of the market the perceived accuracy of return forecasts is high and portfolio managers are therefore willing to go further afield to harvest alpha, while in high-risk states the “unfamiliar” assets are hard to predict and a more concentrated portfolio of assets that are easier to risk manage therefore makes more sense.
I think readers will benefit from the empirical evidence presented in this paper to help them understand how best to handle portfolio construction across different market regimes.
In the third paper in this issue, “Tail protection for long investors: trend convexity at work”, Tung-Lam Dao, Trung-Tu Nguyen, Cyril Deremble, Yves Lemperiere, Jean-Philippe Bouchaud and Marc Potters explore the importance of trend convexity for the tail risk management of long market exposure investment strategies. The authors provide an algorithmic representation of trend-following strategies and demonstrate that their performance can be largely explained by the difference between the long-term and short-term variance (measured under an assumption of zero mean) of the underlying asset returns. The trend is essentially an increase in the long-run variance because the mean, if it is nonzero, contributes to the price differential, while the short-term variance remains relatively unchanged because of the 1= T scale that enters the computation.
Furthermore, the paper proves what some (but not all) researchers and practitioners instinctively know to be true: that trend-following strategies have strongly positive convexity and potentially negative alpha, which is entirely intuitive if one understands that these strategies essentially have option-like payoffs. See, for example, Berd (2010), in which I explained that the trend-following investor essentially bets on the wings of the prospective returns distribution realizing more than statistically expected while the middle of the distribution realizes less, which is the same expectation that an investor trading a straddle would have. Unsurprisingly, trend-following trading strategy dynamically replicates such a payoff. Dao et al’s paper demonstrates this thesis in full detail and quite unambiguously. Furthermore, it goes beyond second-order (volatility/convexity) exposure and also shows a dependence on the third-order (skewness) exposure of the strategy, which is highly nontrivial and has a lot to do with the long-run accumulation of tail risks.
As a corollary to the paper’s findings regarding the statistical signatures of the trending strategies, the authors show that commodity trading advisor strategies provide a natural hedge for downside tail risk for both traditional and risk-parity-weighted long-only investment strategies. This is true even in the absence of positive expected performance. It is even more true, and more attractive from an investor’s point of view, in the light of the well-documented long-term positive performance of trend-following strategies. I concur with the authors that having a reasonably large allocation to such strategies is highly advisable for most investors.
In the issue’s fourth and final paper, “Speed and dimensions of trading”, Boris Gnedenko and Igor Yelnik look at another important aspect of trading strategies. While much attention has been devoted to the risk-based analysis of portfolio composition, there has been much less focus on the risk-based study of trading and turnover. However, for any active strategy these are critical issues, and having only a nominal description of the turnover is clearly an oversight. The authors give a fairly comprehensive treatment of this problem and describe an elegant framework for analysis, deriving metrics such as effective number of trades and effective number of trading dimensions.
The authors’ approach is very compelling: it is certainly natural to think about turnover and trading costs in the same terms as the current composition of the portfolio. And for most quantitative portfolio managers the latter is best described in terms of risk bets, not in terms of asset weights. The turnover of risk bets is therefore also the proper measure for describing trading activity. It allows us to compare, on a like-for-like basis, the predicted transaction costs and the projected excess returns within each effectively independent risk bet. In the process of doing this, the authors naturally develop the invariant metrics that describe the effective number of these risk bets, and the effective number of trades within each risk bet. They represent, respectively, the dimension and the speed of trading; indeed, they represent a very coherent and clear description of the trading activity in a complex portfolio. I found this paper very illuminating and I am sure many of our readers will too.
In conclusion, I hope that this issue will prove to be a useful reference for practitioners and will inspire researchers in industry and academia both to pose more probing questions and to look at those questions from nonstandard angles. Our job at The Journal of Investment Strategies is to promote such diffusion of ideas and a fresh take on problems.
Berd, A. M. (2010). Investment strategy returns: volatility, asymmetry, fat tails and the nature of alpha. In Lessons from the Financial Crisis, A. M. Berd (ed.). Risk Books, London.
Arthur M. Berd
Founder and CEO, General Quantitative LLC
This paper determines life-cycle trading strategies for portfolios subject to the US tax system.
Portfolio concentration and equity market contagion: evidence on the “flight to familiarity” across indexing methods
This paper sheds light on the entanglement of index weighting schemes.
In this paper, the authors show that single-asset trend strategies have built-in convexity, provided their returns are aggregated over the right time scale, ie, that of the trend filter.
In this paper, two new portfolio statistics are introduced: ENT, which measures trading speed, and ENTD, which measures trading diversity. Together with vectors representing major trading directions, these provide new insight into the intrinsic…